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A prototype column generation strategy for the multiple container loading problem

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  • Zhu, Wenbin
  • Huang, Weili
  • Lim, Andrew
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    Abstract

    The multiple container loading cost minimization problem (MCLCMP) is a practical and useful problem in the transportation industry, where products of various dimensions are to be loaded into containers of various sizes so as to minimize the total shipping cost. The MCLCMP can be naturally formulated as a set cover problem and solved using column generation techniques, which is a popular method for handling huge numbers of variables. However, the direct application of column generation is not effective because feasible solutions to the pricing subproblem is required, which for the MCLCMP is NP-hard. We show that efficiency can be greatly improved by generating prototypes that approximate feasible solutions to the pricing problem rather than actual columns. For many hard combinatorial problems, the subproblem in column generation based algorithms is NP-hard; if suitable prototypes can be quickly generated that approximate feasible solutions, then our strategy can also be applied to speed up these algorithms.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 223 (2012)
    Issue (Month): 1 ()
    Pages: 27-39

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    Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:27-39

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Packing; Column generation; Heuristic; Multiple container loading problem;

    References

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    1. Crainic, Teodor Gabriel & Perboli, Guido & Tadei, Roberto, 2009. "TS2PACK: A two-level tabu search for the three-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 195(3), pages 744-760, June.
    2. Eley, Michael, 2002. "Solving container loading problems by block arrangement," European Journal of Operational Research, Elsevier, vol. 141(2), pages 393-409, September.
    3. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    4. Terno, Johannes & Scheithauer, Guntram & Sommerwei[ss], Uta & Riehme, Jan, 2000. "An efficient approach for the multi-pallet loading problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 372-381, June.
    5. Che, Chan Hou & Huang, Weili & Lim, Andrew & Zhu, Wenbin, 2011. "The multiple container loading cost minimization problem," European Journal of Operational Research, Elsevier, vol. 214(3), pages 501-511, November.
    6. Fekete, Sandor P. & van der Veen, Jan C., 2007. "PackLib2: An integrated library of multi-dimensional packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1131-1135, December.
    7. Zhu, Wenbin & Lim, Andrew, 2012. "A new iterative-doubling Greedy–Lookahead algorithm for the single container loading problem," European Journal of Operational Research, Elsevier, vol. 222(3), pages 408-417.
    8. Lodi, Andrea & Martello, Silvano & Vigo, Daniele, 2002. "Heuristic algorithms for the three-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 141(2), pages 410-420, September.
    9. L. R. Ford, Jr. & D. R. Fulkerson, 1958. "A Suggested Computation for Maximal Multi-Commodity Network Flows," Management Science, INFORMS, vol. 5(1), pages 97-101, October.
    10. Bischoff, E. E. & Ratcliff, M. S. W., 1995. "Issues in the development of approaches to container loading," Omega, Elsevier, vol. 23(4), pages 377-390, August.
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